The PV curve shown in the diagram consists of two isothermal and two adiabatic curves. Then:

Question

Given $C_p = a + bT$
$a = 19.5$, $b = 0.042$, $n = 1$ mole
Temperature changes from $27^\circ C$ to $327^\circ C$.
Find $\Delta H$.

Answer 1

To determine the correct relationship between the volumes in the PV diagram, let's analyze the given cyclic process, which consists of two isothermal and two adiabatic processes.

consists of two isothermal and two adiabatic curves

In the given PV diagram:

Process $ ab $ and $ cd $ are adiabatic.
Process $ bc $ and $ da $ are isothermal.

For an adiabatic process, the relationship is given by:

P_1V_1^\gamma = P_2V_2^\gamma

For an isothermal process, the relationship is given by:

P_1V_1 = P_2V_2

Using the cyclic nature of the process, we can equate the work done during the isothermal expansions to that during the compressions:

Considering the isothermal processes:

For the isothermal expansion $ da $ and compression $ bc $, the volume ratios at these steps are equal, so:
$\frac{V_a}{V_d} = \frac{V_b}{V_c}$

This relationship arises because, in a cyclic process, the products of pressures and volumes for isothermal processes must be equal due to Boyle's Law.

Thus, $\frac{V_a}{V_d} = \frac{V_b}{V_c}$ is the correct relationship among the given options.

Answer 2